Is the discovery of Higgs boson contradict the Compositeness model and the preon existence ???!!!
Your discussion style is obtuseDear all
The compositness model was first proposed by A.Salam 1970, mainly due to the hairechary problem, you can read about it in wiki pages.
It is not just Wikipedia. It is the overwhelming consensus of the physics community that there is no evidence for compositeness of leptons and quarks.Perhaps the point is if there is someone here in the forum.who is interested on composites. If nobody can comment beyond the wikipedia, it is probably not worth to raise the topic here.
There is a consensus on the no evidence of substructure. I fact even my esoteric sBootstrap is in the consensus, as it only ask for compositeliness (hey, that is worse!) for the scalar partners of the fermions in a susy theory.It is not just Wikipedia. It is the overwhelming consensus of the physics community that there is no evidence for compositeness of leptons and quarks
I am not sure, I have never seen a proof, besides the *classical* intuition that you mention.If a particle is composite, it has to have a finite radius
Fine example, but that is not all the history. For 1D potentials, we are granted that there is always at least a bound state inside a well, so what happens in the limit of "point-supported potentials" is a single state, if the potential is only supported in one point. Actually the classification of the possible states is equal to the possible boundary conditions, some of then can be produced as limits of potentials going to dirac-delta shapes, some others have other origins. A classic textbook on the topic, by the way, is wrong about the naming of the classification.I'm not sure how I would rigorously prove this for a general case. However, as a model you can use the infinite spherical well potential, so inside the radius the particle is free to move but a very strong restoring force holds the particle in if it tries to leave that radius (also, you do the usual trick of reducing a two body problem to a one body problem). The ground state energy (actually all energy levels) goes as r^-2, where r is the radius of the well. Clearly this diverges when r goes to 0.
The "construction" is that a world-sheet has a bosonic field [itex]X_\mu(\sigma)[/itex] with sigma taking values from a one-dimensional segment, but it does not tell that the projection in the target space, the one where the X maps to, is an extended object. I think that it is clear that for bosonic states it is, with the restriction that it could be "pointlike" in some subset of the coordinates (a "D-brane"). And for fermionic states, I have never seen a clear discussion.But most importantly, there isn't some derived rule that says that the string has to be an extended object, it is the postulated form a particle takes, and thus by construction the string in string theory is extended.